A307890 - OEIS

%I #11 May 17 2024 00:32:54

%S 3677,4073,16447,118463,211217,357131,368153,582017,932413,1172777,

%T 1239443,2284027,2421473,3900931,4943777,5046053,6850463,6966059,

%U 8046347,10448783,11548777,12849937,15198811,16031237,17315087,19443679,20075687,20434811,20462861,20614667

%N Prime centuries with at least one prime year in each decade and exactly one prime year in decades 1 to 8.

%C In other words, prime numbers p such that there are ten consecutive primes between p*100-100 and p*100, each of them in a different decade. (The P-div-10s are all different.) - _Don Reble_, May 02 2019

%e 4073 is in the sequence, representing the prime sequence 407203, 407207, 407219, 407221, 407233, 407249, 407257, 407263, 407273, 407287, 407291, 407299, with 2 primes in decades 0 and 9, and 1 prime in decades 1 to 8. - _R. J. Mathar_, May 03 2019

%p isA307890 := proc(n)

%p     local p, dec ;

%p     if not isprime(n) then

%p         false;

%p     else

%p         p := 100*(n-1) ;

%p         p := prevprime(p+10) ;

%p         for dec from 0 to 9 do

%p             if modp(floor(p/10), 10) <> dec then

%p                 return false;

%p             end if;

%p             p := nextprime(p) ;

%p         end do:

%p         true ;

%p     end if;

%p end proc:

%p for i from 1 do

%p     p := ithprime(i) ;

%p     if isA307890(p) then

%p         printf("%d, \n", p) ;

%p     end if;

%p end do: # _R. J. Mathar_, May 03 2019

%Y Cf. A156115, super set of the primes in A103608.

%K nonn,less

%O 1,1

%A _Zak Seidov_, Feb 27 2009